Hay on Wye is celebrating its 30th anniversary.
Photograph: Keith Morris/Alamy Live News.

Eddie Izzard is in the Spar, wearing leather trousers, four-inch heels and a light smattering of pancake. But this is Hay, so nobody notices. He buys his stuff and totters off down Castle Street, pausing to talk to a dog waiting in the back of a car. Later in the evening, dressed more casually, he will take to the stage to delight an audience.

Hay is like that. The familiar-looking, clean-shaven chap in the linen jacket? (Linen jackets are de rigueur for chaps, this being a literary gathering.) Why it’s Nick Clegg, ex-coalitionista, unexpectedly tall in the flesh. The other tall chap (linen jacket)? Paxo, of course, equally tall. Oh look, there’s Stephen Fry, former National Theatre boss Nick Hytner. It’s like the maxim about the 1960s, that all the people who made the swinging decade would have fitted in one room. Perhaps that’s what Bill Clinton was thinking when he famously decribed the festival as “the Woodstock of the mind”.

This year the Hay Festival turns 30, and is pausing to reflect upon the journey it has taken from its small beginnings around a kitchen table in a market town on the Welsh border to its place as one of the world’s leading literary gatherings, an event that knows no boundaries. Those neglected boundaries are as much physical as psychological: Hay is now a place that exists on several continents. This year the Hay Literary Festival can be found in Colombia, Denmark, Mexico, Spain and Peru; in its 30 years it has travelled to 30 locations.

But it doesn’t really matter where it takes place; Hay is about conversation, ideas, thoughts large and small. By Friday evening, as the festival’s first full day draws to a close, the brain is starting to throb. Themes abound: Brexit, of course, comes up in every conversation, every talk, as does Trump, each treated with a disdain and distaste that is welcomed by the packed crowds of fellow travellers. For Clegg, who is introduced as “one of the most important politicians of our time”, Brexit is “an astonishing self-harming turn in British history”.

Andy Parsons, the comedian brought in to dispatch us into the night with some comedy-fuelled indignation, tests the limits of Hay decorum with a potty-mouthed tirade against the referendum and its aftermath. The lawyer and author Miriam González Durántez – also married to Clegg – delivers an impassioned plea for Europe. “I am a European immigrant,” she declares. “I am a citizen of the world, and therefore I am a citizen of nowhere, in the words of your prime minister.”

Stephen Fry contributes to the ‘Woodstock of the mind’. Photograph: Anna Goldberg

González Durántez’s speech marks the first of 30 “reformations” planned by the festival, a series of interventions and rethinkings “to imagine a better world”, prompted by both the festival’s anniversary and to mark the 500 years since Martin Luther’s 95 Theses. It all sounds very grand: Luther, Hay, the world!

“There wasn’t a vision,” says Peter Florence, the man who as a recent graduate decided with his parents to set up the festival, starting in the garden of a pub, before progressing to the local school and finally a 20-acre site on the edge of the village. “The idea was, let’s make it fun, let’s throw a party and invite some mates around, but it soon got out of hand.”

That party now involves some 250,000 tickets sold to the 500 events held over 10 days in Hay. Children skip along the walkways inside the tented compound, lines snake from the bookshop, criss-crossing other lines waiting for entry to the next event, tangling like kite strings to leave a mass of people expectant, searching for stimulation.

“Who likes science?” comes the shout from one tent. There is a roar, the sound of hundreds of schoolchildren, bussed in from 170 schools, yelling that, yes, they like science. “Who likes chemistry?” the roar is repeated. “Who likes biology?” Again the children shout their approval. Now comes the tricky one: “Who likes psychics?” The gag is met with a chorus of confusion.

But even in this oasis of learning, of erudition, of inquiry, the outside intrudes: armed police mingle, machine guns cradled in their hands. “Are those Tasers or real guns?”, one woman asks her companion.

The enemy here, such as it is, is data. “Stories are so much more powerful than facts and figures,” says Andrew Simms, opening a session that looks to folk tales to help explain our current travails. “That’s not to give an endorsement of the post-fact world in which we live.”

The following morning, the writer Horatio Clare, between readings from his Brecon Beacons Myths & Legends, tells us that “the aural and verbal are under threat from a culture of data”.

With the storm clouds – metaphorical and meteorological – gathering, Florence is in typically ebullient mood, names dripping from his lips: the day that Maya said this, the Coltrane-like cadence of Toni Morrison’s voice, Bill Clinton at 3am, the hole left by the death of Christopher Hitchens – “It’s a black hole!” says Florence – the brilliance of the neuroscientist Hannah Critchlow.

“I’m interested in what the experts think,” he explains, “in deep insight, in specialism. Books are the way we have recorded everything we know. The whole dream here is to make books more accessible by giving them a human context, to take all this extraordinary energy and make it more widely accessible and useful. Writers can touch the parts that politicians and journalists can’t touch. But it starts with the ideas and the story.”